SOLUTION: Verify that tanx cscx/secx=1 is an identity. Write your proof below. Thank you so much for all of your help!!!!! God Bless!!!!!!

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Question 391208: Verify that tanx cscx/secx=1 is an identity. Write your proof below.
Thank you so much for all of your help!!!!!
God Bless!!!!!!
Found 2 solutions by richard1234, Edwin McCravy:
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
We want to show that tan%28x%29csc%28x%29+=+sec%28x%29. Rewriting everything in terms of sin and cos,

%28sin%28x%29%2Fcos%28x%29%29%281%2Fsin%28x%29%29+=+1%2Fcos%28x%29 Cancel out sin(x) to obtain

1%2Fcos%28x%29+=+1%2Fcos%28x%29 which is true for all x that makes the values defined.

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!


The other tutor unfortunately multiplied both sides by sec(x).
That is not allowed in proving identities.  That's because you
cannot multiply both sides by anything until you have proved
that it is an equation.  You can only work with one side at time
when proving an identity.  Here is how to do it working with
only the left side, leaving the right side alone:

tan%28x%29%2Aexpr%28csc%28x%29%2Fsec%28x%29%29=1

Use these three identities:

1.  The quotient identity:    tan%28x%29+=+sin%28x%29%2Fcos%28x%29

2.  The reciprocal identity:  csc%28x%29+=+1%2Fsin%28x%29

3.  The reciprocal identity:  sec%28x%29+=+1%2Fcos%28x%29
 
Substituting:



Simplify the compound fraction by inverting and multiplying



Cancel the sin%28x%29's



Cancel the cos%28x%29's



All that's left is:

        1 = 1

Edwin